The site selection of emergency material reserve point is a key problem to solving the distribution optimization of emergency materials reserve. In this paper, according to the characteristics of emergency material reserves, we comprehensively considered the shortest distance, the shortest time, transportation costs, construction costs, storage quantity and other factors, and established the analysis model to make optimization to the reserve point site selection.
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Manuscript submitted on 09-8-2015 |
Original Manuscript | Study on the Site Selection of Emergency Material Reserve Point |
Emergency material reserve point site selection is a key problem to solving the distribution optimization of emergency material reserve, which is, on the basis of the existing reserve points addresses, according to the possible task, the terrain and traffic conditions, the storage conditions and the allocation of resources, etc., to scientifically determine or adjust the materials reserve distribution, thus, providing more effective material supply for the national material reserve construction and the dealing with emergencies [1R. Zhang, Q. Zhou, and W. Xiong, "Updated A* algorithm and its application", Computer System and Application, vol. A9, pp. 98-107, 2009., 2W. Xiong, and R. Zhang, "A* algorithm and its application in GIS", Computer System and Application, vol. A4, pp. 14-17, 2007.]. Under normal circumstances, the site selection model of emergency material reserve point is established on the basis of the demand situation of variety and quantity from the front supplying points. Then according to the emergency security demand, we select single or multiple emergency material reserves, so that the distribution of emergency material reserves can reach the optimal point. In the premise of meeting emergency material supply, the front time is the shortest, the quantity and quantity of reserves are the most reasonable [3J. Guo, and R. Zhang, "Updated diktra algorithm and its application in GIS", Computer System and Application, vol. A1, pp. 59-62, 2007.].
On the premise that the distance between reserve and the furthest demanding point meets the requirement of material security, the shorter, the better. For instance: emergency material reserve point is at a distance of 150~200 km to the front, within which range it is better to have shorter front distance, the optimization goal is to find the a reserve that has the shortest distance to the demanding point.
If there are multiple reserves, under the situation of same time multiple security, the optimization goal is to find a reserve that has the shortest time to demanding point.
If there is the least transportation cost from a reserve point to each demanding point, it means that there is minimum number of total ton kilometer of material transportation. The goal is for the usual material supply management, to
achieve the purpose of economization.
Emergency material reserve construction cost mainly refers to the construction cost of geography, including buildings, equipment, land and transport distance, etc. This cost is related to the geographical location and the scope of the reserve point.
The emergency material reserve quantity of a reserve point should meet the requirements of sustainable consumption within the time limit. Over the limitation it is wasteful while below the limitation it can not achieve the security requirements.
Because of the continuity of material consumption, we can omit the consideration of the material transportation equipment restrictions. It is acceptable so long as the quantity shipped within the prescribed time limit can meet the emergency security demand.
According to the reserve distribution and production quantity of rear material supplying point, we determine the position, the size and the number of the emergency material reserves [5R.B. Copperman, M.P. Devlin, R.M. Ewalt, T.A. Lockhart, K.D. Peterson, J.H. Lambert, M.L. Tischer, K.P. Spence, K.A. Graham, and W.S. Ferguson, "Coordinating and prioritizing multimodal transportation projects", In: Proceedings of the 2004 IEEE Systems and Information Engineering Design Symposium, IEEE: Charlottesville, VA, 2004, pp. 113-119., 6A. Lozano, and G. Storchi, "Shortest viable path algorithm in multimodal networks", Transportation Quarterly, vol. A35, pp. 225-241, 2001.]. Reserves should have the capacity for continuous supply, and in a long time, the continual material security ability is not necessarily associated with reserve capacity. That is to say, as long as the rear supplying point can provide the latter material supply, the security capacity of emergency material reserve point can avoid the restriction from reserve capacity, and the continual security capacity can be greatly extended. As for the delivery time, materials must be delivered before the end of material consumption, that is, a breaking of supply is not allowed.
The determination of the distribution of emergency material reserve points should be comprehensively considered according to the various modes of transport used here [7J. Guo, Logistics Optimization, Scientific Publishing Company: Beijing, 2010, pp. 225-238.]. And according to the requirements and the characteristics of different modes of transport, arrangement of emergency material reserve point configuration should be reasonable, so that the target of reserve optimization and transportation optimization can be achieved. In addition, in the practical use, not just one single mode of transport is used. Rather, it is usual that many modes of transport are combined together, railway, highway, waterway, etc., are integrated together. Considering this, the shift of mode of transport as well as the road transfer problem must also be taken into account.
We use the general algorithm for the maximum flow in graph theory, to get network feasible flow between reserves and demanding points in the network. It is also the maximum flow through the road network, and its condition of equilibrium is in each intermediate point, the total amount of material imported equals to total goods exported. Then according to emergency conditions of other transport tasks, the passable flow of material transportation can be determined [8R. Yu, and J. Wang, "Research on combination optimization of multimodal transportation system of containers", System Simulation Technology, vol. A4, pp. 272-275, 2009.].
We can set D= (V, E, C(e), vs, vt) as a capacity network for emergency material transportation, and set two specific points in D. One is called the starting point of emergency materials, denoted as vs; the other is called the receiver (demanding point), denoted as vt. Other points in D are called the intermediate points. If f = (fij) is a feasible flow on network D, then the following two conditions should be satisfied:
(1) |
The question is to get the feasible flow that can make v(f) reach the maximum on D, this feasible flow is the maximum flow of the network.
The key of the implementation of emergency material reserve point site selection is the determination of the alternative emergency material reserve. The establishment of an alternative emergency material reserve point should consider factors such as reserve conditions, traffic conditions, safety and the difficulty of supplement, etc. Not all the positions that can establish material base stations can be alternative reserve points.
According to the different tasks and the material sources, alternative reserve points are selected. The selection of the alternative point has a direct impact on the optimal scheme and calculation and operation costs. If there are too much alternatives, it will make the model more complex and the computational workload will be increased; while if there are too little alternatives, it may make the optimization scheme far away from the optimal solution, then it will not be up to the purpose of reasonable distribution.
After the determination of alternative emergency material reserve points, specific analysis and comprehensive evaluation on each alternative should then be carried out, from the point of view of the overall benefits, weighting the size of function of the alternative points in the distribution. Evaluation indexes include [9C. Gang, B. Liu, and S. Kai, "Research on the selection of adaptive optimal transportation modes based on gray evaluation theory", Mathematics in Practice and Theory, vol. A3, pp. 57-63, 2007.]:
We set A1, A2, ... , Am, is the number m evaluation schemes. X1, X2, ... , Xn is the number n evaluation index of the alternative scheme of evaluation. W1, W2, ... , Wn is the number n weighing of evaluation index. Vi1, Vi2, ... , Vin is the number i alternative scheme concerning value assessment of Xj index (j=1, 2,... n). The relative correlation matrix is shown in Table 1.
(2) |
For different evaluation indexes, it is difficult to compare in the same standard, because the convenient transport hubs are often in poor hidden conditions, the reserve position that near the front are usually poorly secured, those areas that are convenient for material supply are often geographically distant from front supplementing points [10Y. Hao, Logistic Management Optimization, Scientific Publishing Company: Beijing, 2003, pp. 217-218.]. In this case, pair comparison can be used on different evaluation indexes for weighting, which is, to make assessment on alternative schemes, basing on a certain standard while using all the evaluation indexes. comprehensive evaluation value by the weighted method of evaluation of alternatives, then to make comprehensive evaluation on all the evaluation indexes of alternative schemes by using the method of weighting.
After pair comparison on the evaluation indexes, we think that the relative important indexes get score of 1, the relative less important indexes get score of 0. In this way, the evaluation indexes weightings after comparison are shown in Table 2 [11R. Zhang, and H. Xu, "Study on optimization model of materials transptort way", China Storage & Transport, vol. A4, pp. 95-97, 2009.].
After getting the weighting value of evaluation indexes, then we made comprehensive evaluations on each alternative reserve point, and the criteria are classified into: good, average, bad. For instance, the evaluations on 8 alternative emergency material reserves are shown in Table 3.
According to the evaluation of each alternative point, the good get scores of 2, the average get 1, the bad get 0. In this way, the alternative points scores are shown in Table 4.
According to Table 4 the scores of each reserve point are:
b1:2×0.3+1×0.3+1×0.2+2×0.1+0×0.1=1.3
b2:0×0.3+0×0.3+2×0.2+1×0.1+0×0.1=0.5
b3:1×0.3+1×0.3+1×0.2+1×0.1+1×0.1=1.0
b4:2×0.3+2×0.3+0×0.2+2×0.1+0×0.1=1.4
b5:1×0.3+2×0.3+1×0.2+0×0.1+2×0.1=1.3
b6:1×0.3+2×0.3+0×0.2+0×0.1+2×0.1=1.1
b7:0×0.3+0×0.3+2×0.2+0×0.1+1×0.1=0.5
b8:0×0.3+1×0.3+1×0.2+1×0.1+1×0.1=0.7
According to the comprehensive evaluation on the below alternatives, we can omit some alternatives that cannot meet the requirements of an emergency material reserve, so that to reduce the complexity of subsequent model. For example taking the evaluation score of 1 as the standard, if the score is greater than 1 then it can be taken as an alternative point, if the score is less than 1 then it can not be taken as an alternative point. In this way, alternative b2, b7, b8, which meet the requirement, can be removed, while the remaining 5 alternative points are reserved [12R. Zhang, and Q. Liu, "Study on transport optimization model and application", Logistics Techniques, vol. A3, pp. 85-87, 2009.].
In practical application, there are different site selection criteria on the assemble scheme of emergency material reserves. We consider using multi-objective decision making method, comprehensively considering the factors as emergency material reserve distance, time, transport cost, construction cost, reserves number, etc., and to give different weighted coefficient and then to get the optimal scheme of emergency material reserves.
Firstly we need to determine the purpose of evaluation and the establishment of evaluation index. The evaluation index can be established through expert scoring and the comprehensive review; alternative schemes can be determined by review from policy-makers and experts.
According to the evaluation index and evaluation purposes, as well as the alternative schemes, the analysis model is established. See in Fig. (1).
Fig. (1) The emergency material reserve optimization level model. |
As can be seen from the graph, measurement criteria of each evaluation unit is different, including distance, time, cost, quantity and so on, which makes it unable to make comparison. Therefore, we must transfer the values of these units into the comparable utility value to represent. The utility value is all the numbers of 0 to 1, the utility value of the worst level of each target is 0, eliminating the ones lower than the worst; the utility value of the worst level of each target is 1, taking the ones higher than the best as the same level of the best and get a value of 1.
Thus, we can draw the utility curve of each target, and calculate out the utility value of each target in each scheme. In this way, the curve of utility value taking distance as the optimization objective are shown in Fig. (2).
Fig. (2) The curve of utility value taking distance as the optimization objective. |
In this way, the curve of utility value taking time as optimization target are shown in Fig. (3).
Fig. (3) The curve of utility value taking time as the optimization objective. |
In this way, the curve of utility value taking transport cost as optimization target are shown in Fig. (4).
Fig. (4) The curve of utility value taking transport cost as the optimization objective. |
In this way, the curve of utility value taking construction cost as optimization target are shown in Fig. (5).
Fig. (5) The curve of utility value taking construction cost as the optimization objective. |
In this way, the curve of utility value taking reserve number as optimization target are shown in Fig. (6).
Taken as a alternative scheme, if there is one in all the target that surpass the worst degree, then it will be taken as a bad case for omitting.
In the above targets, not all the targets are of equal importance, therefore we need to consider the degree of importance of each target in optimization and give it appropriate coefficient.
Fig. (6) The curve of utility value taking reserve number as optimization target. |
In the above targets, not all the targets are of equal importance, therefore we need to consider the degree of importance of each target in optimization and give it appropriate coefficient.
(3) |
Suppose there are P1, P2, P3, the distribution scheme, we comprehensively take into consideration optimization targets--- the shortest distance, the minimum time, the minimum cost, and minimum construction cost and the minimum reserve number, etc., to make comparing optimization of emergency material reserve. The 3 reserve scheme target values are shown in Table 5.
According to the utility degree set above, utility value calculation is made and we get result shown in Table 6.
From the table we can see when using the scheme of P1, multi-target utility value gets the maximum, i.e., the optimal reserve effectiveness can get. So the optimal result of multi-target decision making is selection scheme of P1.
The optimization model above is the optimization of multi-condition and multi-target in general circumstances, multi-objective. We can see from the optimization target that some optimization targets may be contradictory. As for solving these questions, generally there is no optimal solution existed. In a range of feasible solution, calculating by fuzzy logic multi-target genetic algorithm, we can receive a better efficiency.
The authors confirm that this article content has no conflict of interest.
This work is supported by the Education Science fund of the Military Science Institute of Beijing, China (No.2013JY368).